Abstract

We report the first demonstration of high bit rate signal processing by a fiber-based photonic wire. We achieve 160Gb/s demultiplexing via four wave mixing in a 1.9μm diameter photonic wire tapered from As2S3 chalcogenide glass single mode fibre, with very low pump power requirements (< 20mW average power, 0.45W peak power), enabled by a very high nonlinearity (γ ~ 7850 W-1 km-1) and greatly reduced dispersion.

© 2008 Optical Society of America

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  1. B. J. Eggleton, S. Radic, and D. J. Moss, “Nonlinear Optics in Communications: From Crippling Impairment to Ultrafast Tools” in Optical Fiber Telecommunications V: Components and Sub-systems, Ivan P. Kaminow, Tingye Li, and Alan E. Willner, ed. (Academic Press, Oxford, UK, February 2008),Chap. 20.
  2. V. G. Ta’eed, M. Shokooh-Saremi, L. B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. L. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005).
    [Crossref] [PubMed]
  3. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
    [Crossref]
  4. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41, 320–321 (2005).
    [Crossref]
  5. S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
    [Crossref]
  6. B. E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
    [Crossref]
  7. M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
    [Crossref]
  8. M. D. Pelusi, V. G. Ta’eed, M. R. E. Lamont, S. Madden, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Ultra-high Nonlinear As2S3 planar waveguide for 160-Gb/s optical time-division demultiplexing by four-wave mixing,” IEEE Photon. Technol. Lett. 19, 1496–1498 (2007).
    [Crossref]
  9. K. Inoue and H. Toba, “Wavelength conversion experiment using fiber 4-wave-mixing,” IEEE Photon. Technol. Lett. 4, 69–72 (1992).
    [Crossref]
  10. B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
    [Crossref]
  11. J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
    [Crossref]
  12. V. G. Ta’eed, L. B. Fu, M. Pelusi, M. Rochette, I. C. M. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express 14, 10371–10376 (2006).
    [Crossref] [PubMed]
  13. L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
    [Crossref]
  14. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
    [Crossref] [PubMed]
  15. V. G. Ta’eed, N. J. Baker, L. B. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15, 9205–9221 (2007).
    [Crossref] [PubMed]
  16. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
    [Crossref] [PubMed]
  17. R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
    [Crossref] [PubMed]
  18. T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36, 467–495 (2006).
    [Crossref]
  19. E. C. Mägi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers,” Opt. Express 15, 10324–10329 (2007).
    [Crossref] [PubMed]
  20. D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. B. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
    [Crossref] [PubMed]
  21. B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.
  22. N. Vukovic, N.G. R. Broderick, M. Petrovich, and G. Brambilla, “Fabrication of Metre-long Fibre Tapers”, in Conference for Lasers and Electro-Optics, (San Jose, California, May 2008), paper CThV5.
  23. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, California, 2001).
  24. J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
    [Crossref]
  25. E. C. Magi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express 12, 776–784 (2004).
    [Crossref] [PubMed]

2008 (5)

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
[Crossref]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[Crossref] [PubMed]

D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. B. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
[Crossref] [PubMed]

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

2007 (3)

2006 (4)

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

V. G. Ta’eed, L. B. Fu, M. Pelusi, M. Rochette, I. C. M. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express 14, 10371–10376 (2006).
[Crossref] [PubMed]

R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[Crossref] [PubMed]

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

2005 (2)

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41, 320–321 (2005).
[Crossref]

V. G. Ta’eed, M. Shokooh-Saremi, L. B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. L. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (2)

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

2001 (1)

B. E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

2000 (1)

B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
[Crossref]

1995 (1)

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

1992 (1)

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber 4-wave-mixing,” IEEE Photon. Technol. Lett. 4, 69–72 (1992).
[Crossref]

Aggarwal, I. D.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, California, 2001).

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Baker, N. J.

Bashkansky, M.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Belardi, W.

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

Bergman, K.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Biberman, A.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Blumenthal, D. J.

B. E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
[Crossref]

Bogoni, A.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Brambilla, G.

N. Vukovic, N.G. R. Broderick, M. Petrovich, and G. Brambilla, “Fabrication of Metre-long Fibre Tapers”, in Conference for Lasers and Electro-Optics, (San Jose, California, May 2008), paper CThV5.

Broderick, N.G. R.

N. Vukovic, N.G. R. Broderick, M. Petrovich, and G. Brambilla, “Fabrication of Metre-long Fibre Tapers”, in Conference for Lasers and Electro-Optics, (San Jose, California, May 2008), paper CThV5.

Calabretta, N.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Choi, D. Y.

M. D. Pelusi, V. G. Ta’eed, M. R. E. Lamont, S. Madden, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Ultra-high Nonlinear As2S3 planar waveguide for 160-Gb/s optical time-division demultiplexing by four-wave mixing,” IEEE Photon. Technol. Lett. 19, 1496–1498 (2007).
[Crossref]

V. G. Ta’eed, N. J. Baker, L. B. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15, 9205–9221 (2007).
[Crossref] [PubMed]

Dutton, Z.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Ebendorff-Heidepriem, H.

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

Eggleton, B. J.

D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. B. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
[Crossref] [PubMed]

L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
[Crossref]

M. D. Pelusi, V. G. Ta’eed, M. R. E. Lamont, S. Madden, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Ultra-high Nonlinear As2S3 planar waveguide for 160-Gb/s optical time-division demultiplexing by four-wave mixing,” IEEE Photon. Technol. Lett. 19, 1496–1498 (2007).
[Crossref]

E. C. Mägi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers,” Opt. Express 15, 10324–10329 (2007).
[Crossref] [PubMed]

V. G. Ta’eed, N. J. Baker, L. B. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15, 9205–9221 (2007).
[Crossref] [PubMed]

V. G. Ta’eed, L. B. Fu, M. Pelusi, M. Rochette, I. C. M. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express 14, 10371–10376 (2006).
[Crossref] [PubMed]

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41, 320–321 (2005).
[Crossref]

V. G. Ta’eed, M. Shokooh-Saremi, L. B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. L. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005).
[Crossref] [PubMed]

E. C. Magi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express 12, 776–784 (2004).
[Crossref] [PubMed]

B. J. Eggleton, S. Radic, and D. J. Moss, “Nonlinear Optics in Communications: From Crippling Impairment to Ultrafast Tools” in Optical Fiber Telecommunications V: Components and Sub-systems, Ivan P. Kaminow, Tingye Li, and Alan E. Willner, ed. (Academic Press, Oxford, UK, February 2008),Chap. 20.

Finsterbusch, K.

Florea, C. M.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Foster, M. A.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[Crossref] [PubMed]

Foster, M.A.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Fresi, F.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Fu, L.

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41, 320–321 (2005).
[Crossref]

Fu, L. B.

L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
[Crossref]

D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. B. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33, 660–662 (2008).
[Crossref] [PubMed]

V. G. Ta’eed, N. J. Baker, L. B. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15, 9205–9221 (2007).
[Crossref] [PubMed]

E. C. Mägi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers,” Opt. Express 15, 10324–10329 (2007).
[Crossref] [PubMed]

V. G. Ta’eed, L. B. Fu, M. Pelusi, M. Rochette, I. C. M. Littler, D. J. Moss, and B. J. Eggleton, “Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber,” Opt. Express 14, 10371–10376 (2006).
[Crossref] [PubMed]

V. G. Ta’eed, M. Shokooh-Saremi, L. B. Fu, D. J. Moss, M. Rochette, I. C. M. Littler, B. J. Eggleton, Y. L. Ruan, and B. Luther-Davies, “Integrated all-optical pulse regenerator in chalcogenide waveguides,” Opt. Lett. 30, 2900–2902 (2005).
[Crossref] [PubMed]

Gaeta, A. L.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[Crossref] [PubMed]

Gaeta, A.L.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Gattass, R. R.

R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[Crossref] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Geraghty, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

Guglielmucci, M.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Ibsen, M.

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

Inoue, K.

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber 4-wave-mixing,” IEEE Photon. Technol. Lett. 4, 69–72 (1992).
[Crossref]

Kamatani, O.

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

Kawanishi, S.

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

Lamont, M. R. E.

Lee, B.G.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Lee, J. H.

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

Lipson, M.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[Crossref] [PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Littler, I.

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41, 320–321 (2005).
[Crossref]

Littler, I. C. M.

Lou, J. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Luther-Davies, B.

Madden, S.

M. D. Pelusi, V. G. Ta’eed, M. R. E. Lamont, S. Madden, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Ultra-high Nonlinear As2S3 planar waveguide for 160-Gb/s optical time-division demultiplexing by four-wave mixing,” IEEE Photon. Technol. Lett. 19, 1496–1498 (2007).
[Crossref]

V. G. Ta’eed, N. J. Baker, L. B. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D. Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15, 9205–9221 (2007).
[Crossref] [PubMed]

Magi, E. C.

L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
[Crossref]

E. C. Magi, P. Steinvurzel, and B. J. Eggleton, “Tapered photonic crystal fibers,” Opt. Express 12, 776–784 (2004).
[Crossref] [PubMed]

Mägi, E. C.

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Mazur, E.

R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[Crossref] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Meloni, G.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Monro, T. M.

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

Morioka, T.

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

Moss, D. J.

Nguyen, H. C.

Nguyen, V. Q.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Ohlen, P.

B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
[Crossref]

Olsson, B. E.

B. E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
[Crossref]

Pelusi, M.

Pelusi, M. D.

L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
[Crossref]

M. D. Pelusi, V. G. Ta’eed, M. R. E. Lamont, S. Madden, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Ultra-high Nonlinear As2S3 planar waveguide for 160-Gb/s optical time-division demultiplexing by four-wave mixing,” IEEE Photon. Technol. Lett. 19, 1496–1498 (2007).
[Crossref]

Petrovich, M.

N. Vukovic, N.G. R. Broderick, M. Petrovich, and G. Brambilla, “Fabrication of Metre-long Fibre Tapers”, in Conference for Lasers and Electro-Optics, (San Jose, California, May 2008), paper CThV5.

Poti, L.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Pureza, P.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Radic, S.

B. J. Eggleton, S. Radic, and D. J. Moss, “Nonlinear Optics in Communications: From Crippling Impairment to Ultrafast Tools” in Optical Fiber Telecommunications V: Components and Sub-systems, Ivan P. Kaminow, Tingye Li, and Alan E. Willner, ed. (Academic Press, Oxford, UK, February 2008),Chap. 20.

Rau, L.

B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
[Crossref]

Richardson, D. J.

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

Rochette, M.

Roelens, M. A. F.

Ruan, Y. L.

Salem, R.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

Sanghera, J. S.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Saruwatari, M.

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

Scaffardi, M.

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Shaw, L. B.

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Shokooh-Saremi, M.

Steinvurzel, P.

Svacha, G. T.

Ta’eed, V. G.

Takara, H.

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

Toba, H.

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber 4-wave-mixing,” IEEE Photon. Technol. Lett. 4, 69–72 (1992).
[Crossref]

Tong, L. M.

R. R. Gattass, G. T. Svacha, L. M. Tong, and E. Mazur, “Supercontinuum generation in submicrometer diameter silica fibers,” Opt. Express 14, 9408–9414 (2006).
[Crossref] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Turner, A. C.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300–1320 (2008).
[Crossref] [PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

Turner, A.C.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

Vukovic, N.

N. Vukovic, N.G. R. Broderick, M. Petrovich, and G. Brambilla, “Fabrication of Metre-long Fibre Tapers”, in Conference for Lasers and Electro-Optics, (San Jose, California, May 2008), paper CThV5.

Yeom, D. I.

Yusoff, Z.

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

Annu. Rev. Mater. Res. (1)

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Annu. Rev. Mater. Res. 36, 467–495 (2006).
[Crossref]

Electron. Lett. (3)

L. B. Fu, M. D. Pelusi, E. C. Magi, V. G. Ta’eed, and B. J. Eggleton, “Broadband all-optical wavelength conversion of 40 Gbit/s signals in nonlinearity enhanced tapered chalcogenide fibre,” Electron. Lett. 44, 44–45 (2008).
[Crossref]

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41, 320–321 (2005).
[Crossref]

S. Kawanishi, H. Takara, T. Morioka, O. Kamatani, and M. Saruwatari, “200Gbit/s, 100km time-division-multiplexed optical-transmission using supercontinuum pulses with prescaled PLL timing extraction and all-optical demultiplexing,” Electron. Lett. 31, 816–817 (1995).
[Crossref]

IEEE Photon. Technol. Lett. (5)

B. E. Olsson and D. J. Blumenthal, “All-optical demultiplexing using fiber cross-phase modulation (XPM) and optical filtering,” IEEE Photon. Technol. Lett. 13, 875–877 (2001).
[Crossref]

M. D. Pelusi, V. G. Ta’eed, M. R. E. Lamont, S. Madden, D. Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Ultra-high Nonlinear As2S3 planar waveguide for 160-Gb/s optical time-division demultiplexing by four-wave mixing,” IEEE Photon. Technol. Lett. 19, 1496–1498 (2007).
[Crossref]

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber 4-wave-mixing,” IEEE Photon. Technol. Lett. 4, 69–72 (1992).
[Crossref]

B. E. Olsson, P. Ohlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000).
[Crossref]

J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, “A tunable WDM wavelength converter based on cross-phase modulation effects in normal dispersion holey fiber,” IEEE Photon. Technol. Lett. 15, 437–439 (2003).
[Crossref]

J. Non-Cryst. Solids (1)

J. S. Sanghera, C. M. Florea, L. B. Shaw, P. Pureza, V. Q. Nguyen, M. Bashkansky, Z. Dutton, and I. D. Aggarwal, “Non-linear properties of chalcogenide glasses and fibers,” J. Non-Cryst. Solids 354, 462–467 (2008).
[Crossref]

Nat. Photonics (1)

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426, 816–819 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Scaffardi, F. Fresi, G. Meloni, A. Bogoni, L. Poti, N. Calabretta, and M. Guglielmucci, “Ultra-fast 160 : 10 Gbit/s time demultiplexing by four wave mixing in 1 m-long B2O3-based fiber,” Opt. Commun. 268, 38–41 (2006).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Other (4)

B. J. Eggleton, S. Radic, and D. J. Moss, “Nonlinear Optics in Communications: From Crippling Impairment to Ultrafast Tools” in Optical Fiber Telecommunications V: Components and Sub-systems, Ivan P. Kaminow, Tingye Li, and Alan E. Willner, ed. (Academic Press, Oxford, UK, February 2008),Chap. 20.

B.G. Lee, A. Biberman, M.A. Foster, A.C. Turner, M. Lipson, A.L. Gaeta, and K. Bergman, “Bit-error-rate characterization of silicon four wave mixing wavelength converters at 10 and 40 Gb/s,” in Conference for Lasers and Electro-Optics, (San Jose, California, USA, May 2008), post-deadline paper CPDB4.

N. Vukovic, N.G. R. Broderick, M. Petrovich, and G. Brambilla, “Fabrication of Metre-long Fibre Tapers”, in Conference for Lasers and Electro-Optics, (San Jose, California, May 2008), paper CThV5.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, California, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

Principle of all-optical time-division demultiplexing an optical signal to obtain a lower bit rate tributary by four wave mixing with a pump pulse train of sub-harmonic repetition

Fig. 2.
Fig. 2.

FEM calculations of a) total dispersion (at 1550 nm) and b) effective mode area, Aeff, and nonlinearity coefficient, γ, versus As2S3 glass fiber waist diameter.

Fig. 3.
Fig. 3.

Schematic of As2S3 chalcogenide glass based fiber photonic “wire”, with 1.9 μm outer diameter and 5cm in length. The central image is an SEM picture of the photonic wire.

Fig. 5.
Fig. 5.

(a) Output optical spectrum showing generation of 10 Gb/s idler at 1540 nm via FWM between 10 GHz pump and 160 Gb/s signal. (inset) 10 Gb/s signal eye diagram of idler after optical filtering, measured using a 65 GHz bandwidth detector and electrical sampling scope. (b) Optical sampling scope measurements of (top) 160 Gb/s signal at input and (lower) output of the taper showing recovery of 10 Gb/s tributary after optical filtering.

Fig. 4.
Fig. 4.

Experimental set-up for optical time-division demultiplexing a 160 Gb/s signal to 10 Gb/s via FWM in a As2S3 photonic wire.

Fig. 6.
Fig. 6.

Conversion efficiency from signal to idler wavelengths via FWM in a lossless 5 cm length waveguide (Eq. [2]) using data from Fig. 2 for γ and β2 at the pump wavelength, for a 10 nm pump and signal wavelength separation and different pump powers of 0.45 W (solid curve), 2 W (dashed curve) and 4 W (dotted curve)

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

L coh = 2 π k 2 π Δ β 2 π β 2 · Ω s 2
G c = ( γ · P p g ) 2 · sin 2 ( g · L )
g 2 = Δ β ( Δ β 4 + γ P p )

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